- #1

rbzima

- 84

- 0

_{n}) and (b

_{n}) are Cauchy sequences, then (c

_{n}) = |a

_{n}- b

_{n}| is also a Cauchy sequence.

I know that the triangle inequality is going to be used at one point or another, but I suppose I'm a little confused because:

(a

_{n}) is Cauchy implies |a

_{n}- a

_{m}| < e

(b

_{n}) is Cauchy implies |b

_{n}- b

_{m}| < e

I think at some point my e's are going to be changed to e/2, which is totally legitimate because e is arbitrary anyway.